public static int SelectLevels(number[] x, int[][] J, int Kmin, int Kmax, double[] BIC)
{
int N = x.Length;
if (Kmin >= Kmax || N < 2)
{
return(Math.Min(Kmin, Kmax));
}
if (BIC.Length != Kmax - Kmin + 1)
{
Array.Resize(ref BIC, Kmax - Kmin + 1);
}
// double variance_min, variance_max;
// range_of_variance(x, variance_min, variance_max);
int Kopt = Kmin;
double maxBIC = 0;
double[] lambda = new double[Kmax];
number[] mu = new number[Kmax];
number[] sigma2 = new number[Kmax];
double[] coeff = new double[Kmax];
for (int K = Kmin; K <= Kmax; ++K)
{
int[] size = new int[K];
// Backtrack the matrix to determine boundaries between the bins.
DynamicProgramming.Backtrack(x, J, size, K);
int indexLeft = 0;
int indexRight;
for (int k = 0; k < K; ++k)
{ // Estimate GMM parameters first
lambda[k] = size[k] / (double)N;
indexRight = indexLeft + size[k] - 1;
ShiftedDataVariance(x, indexLeft, indexRight, out mu[k], out sigma2[k]);
if (sigma2[k] == 0 || size[k] == 1)
{
number dmin;
if (indexLeft > 0 && indexRight < N - 1)
{
dmin = Math.Min(x[indexLeft] - x[indexLeft - 1], x[indexRight + 1] - x[indexRight]);
}
else if (indexLeft > 0)
{
dmin = x[indexLeft] - x[indexLeft - 1];
}
else
{
dmin = x[indexRight + 1] - x[indexRight];
}
// std::cout << "sigma2[k]=" << sigma2[k] << "==>";
if (sigma2[k] == 0)
{
sigma2[k] = dmin * dmin / ((number)4) / ((number)9);
}
if (size[k] == 1)
{
sigma2[k] = dmin * dmin;
}
// std::cout << sigma2[k] << std::endl;
}
/*
* if(sigma2[k] == 0) sigma2[k] = variance_min;
* if(size[k] == 1) sigma2[k] = variance_max;
*/
coeff[k] = lambda[k] / Math.Sqrt((double)(2 * PI * sigma2[k]));
indexLeft = indexRight + 1;
}
double loglikelihood = 0;
for (int i = 0; i < N; ++i)
{
double L = 0;
for (int k = 0; k < K; ++k)
{
L += coeff[k] * Math.Exp((double)(-(x[i] - mu[k]) * (x[i] - mu[k]) / (2 * sigma2[k])));
}
loglikelihood += Math.Log(L);
}
// Compute the Bayesian information criterion
BIC[K - Kmin] = 2d * loglikelihood - (3d * K - 1d) * Math.Log(N); //(K*3-1)
double bic = BIC[K - Kmin];
// std::cout << "k=" << K << ": Loglh=" << loglikelihood << ", BIC=" << BIC << std::endl;
if (K == Kmin)
{
maxBIC = bic;
Kopt = Kmin;
}
else
{
if (bic > maxBIC)
{
maxBIC = bic;
Kopt = K;
}
}
}
return(Kopt);
}
public static int SelectLevels(number[] x, number[] y, int[][] J, int Kmin, int Kmax, double[] BIC)
{
int N = x.Length;
/*if (Kmin == Kmax)
* {
* return Kmin;
* }*/
if (Kmin > Kmax || N < 2)
{
return(Math.Min(Kmin, Kmax));
}
if (BIC.Length != Kmax - Kmin + 1)
{
Array.Resize(ref BIC, Kmax - Kmin + 1);
}
// double variance_min, variance_max;
// range_of_variance(x, variance_min, variance_max);
int Kopt = Kmin;
double maxBIC = 0;
number[] lambda = new number[Kmax];
number[] mu = new number[Kmax];
number[] sigma2 = new number[Kmax];
double[] coeff = new double[Kmax];
int[] counts = new int[Kmax];
number[] weights = new number[Kmax];
for (int K = Kmin; K <= Kmax; ++K)
{
// std::vector< std::vector< size_t > > JK(J.begin(), J.begin()+K);
// Backtrack the matrix to determine boundaries between the bins.
DynamicProgramming.BacktrackWeighted(x, y, J, counts, weights, K);
// double totalweight = std::accumulate(weights.begin(), weights.begin() + K, 0, std::plus<double>());
number totalweight;
totalweight = 0;
for (int k = 0; k < K; k++)
{
totalweight += weights[k];
}
int indexLeft = 0;
int indexRight;
for (int k = 0; k < K; ++k)
{ // Estimate GMM parameters first
lambda[k] = weights[k] / totalweight;
indexRight = indexLeft + counts[k] - 1;
ShiftedDataVariance(x, y, weights[k], indexLeft, indexRight, out mu[k], out sigma2[k]);
if (sigma2[k] == 0 || counts[k] == 1)
{
number dmin;
if (indexLeft > 0 && indexRight < N - 1)
{
dmin = Math.Min(x[indexLeft] - x[indexLeft - 1], x[indexRight + 1] - x[indexRight]);
}
else if (indexLeft > 0)
{
dmin = x[indexLeft] - x[indexLeft - 1];
}
else
{
dmin = x[indexRight + 1] - x[indexRight];
}
// std::cout << "sigma2[k]=" << sigma2[k] << "==>";
if (sigma2[k] == 0)
{
sigma2[k] = (dmin * dmin) / (number)4 / (number)9;
}
if (counts[k] == 1)
{
sigma2[k] = (dmin * dmin);
}
// std::cout << sigma2[k] << std::endl;
}
/*
* if(sigma2[k] == 0) sigma2[k] = variance_min;
* if(size[k] == 1) sigma2[k] = variance_max;
*/
coeff[k] = (double)lambda[k] / Math.Sqrt((double)(2 * PI * sigma2[k]));
indexLeft = indexRight + 1;
}
double loglikelihood = 0;
for (int i = 0; i < N; ++i)
{
double L = 0;
for (int k = 0; k < K; ++k)
{
L += (coeff[k]) * Math.Exp((double)(-(x[i] - mu[k]) * (x[i] - mu[k]) / (2 * sigma2[k])));
}
loglikelihood += ((double)y[i]) * Math.Log(L);
}
// double & bic = BIC[K-Kmin];
// Compute the Bayesian information criterion
double bic = 2 * loglikelihood - (3 * K - 1) * Math.Log((double)totalweight); //(K*3-1)
// std::cout << "k=" << K << ": Loglh=" << loglikelihood << ", BIC=" << BIC << std::endl;
if (K == Kmin)
{
maxBIC = bic;
Kopt = Kmin;
}
else
{
if (bic > maxBIC)
{
maxBIC = bic;
Kopt = K;
}
}
BIC[K - Kmin] = bic;
}
return(Kopt);
}
private static void KMeans(number[] x, number[] y, int Kmin, int Kmax, out int[] clusters, out number[] centers, out number[] withinss, out number[] size, out double[] BIC, Method method, DissimilarityType criterion)
{
// Input:
// x -- an array of double precision numbers, not necessarily sorted
// Kmin -- the minimum number of clusters expected
// Kmax -- the maximum number of clusters expected
// NOTE: All vectors in this program is considered starting at position 0.
int N = x.Length;
clusters = new int[N];
BIC = new double[Kmax - Kmin];
int[] order = new int[N];
for (int i = 0; i < order.Length; ++i)
{
order[i] = i;
}
bool is_sorted = true;
for (int i = 0; i < N - 1; ++i)
{
if (x[i] > x[i + 1])
{
is_sorted = false;
break;
}
}
number[] x_sorted = null;
number[] y_sorted = null;
bool is_equally_weighted = true;
if (!is_sorted)
{
x_sorted = new number[x.Length];
Array.Copy(x, x_sorted, x.Length);
Array.Sort(x_sorted, order);
for (int i = 0; i < x_sorted.Length; i++)
{
x_sorted[i] = x[order[i]];
}
}
else
{
x_sorted = x;
}
// check to see if unequal weight is provided
if (y != null)
{
is_equally_weighted = true;
for (int i = 1; i < N; ++i)
{
if (y[i] != y[i - 1])
{
is_equally_weighted = false;
break;
}
}
}
if (!is_equally_weighted)
{
y_sorted = new number[N];
for (int i = 0; i < N; ++i)
{
y_sorted[i] = y[order[i]];
}
}
else
{
y = null;
}
int nUnique = 1;
if (N == 0)
{
nUnique = 0;
}
if (N > 1)
{
for (int i = 1; i < N; i++)
{
if (x_sorted[i - 1] != x_sorted[i])
{
nUnique++;
}
}
}
Kmax = nUnique < Kmax ? nUnique : Kmax;
if (nUnique > 1)
{ // The case when not all elements are equal.
number[][] S = new number[Kmax][];
for (int i = 0; i < Kmax; i++)
{
S[i] = new number[N];
}
int[][] J = new int[Kmax][];
for (int i = 0; i < Kmax; i++)
{
J[i] = new int[N];
}
int Kopt;
DynamicProgramming.FillMatrix(x_sorted, y_sorted, S, J, method, criterion);
// Fill in dynamic programming matrix
if (is_equally_weighted)
{
Kopt = NonWeighted.SelectLevels(x_sorted, J, Kmin, Kmax, BIC);
}
else
{
switch (criterion)
{
case DissimilarityType.L2Y:
Kopt = NonWeighted.SelectLevels(y_sorted, J, Kmin, Kmax, BIC);
break;
default:
Kopt = Weighted.SelectLevels(x_sorted, y_sorted, J, Kmin, Kmax, BIC);
break;
}
}
centers = new number[Kopt];
withinss = new number[Kopt];
size = new number[Kopt];
if (Kopt < Kmax)
{ // Reform the dynamic programming matrix S and J
Array.Resize(ref J, Kopt);
}
int[] cluster_sorted = new int[N];
// Backtrack to find the clusters beginning and ending indices
if (is_equally_weighted && criterion == DissimilarityType.L1)
{
DynamicProgramming.BacktrackL1(x_sorted, J, cluster_sorted, centers, withinss, size);
}
else if (is_equally_weighted && criterion == DissimilarityType.L2)
{
DynamicProgramming.Backtrack(x_sorted, J, cluster_sorted, centers, withinss, size);
}
else if (criterion == DissimilarityType.L2Y)
{
DynamicProgramming.BacktrackL2Y(x_sorted, y_sorted, J, cluster_sorted, centers, withinss, size);
}
else
{
DynamicProgramming.BacktrackWeighted(x_sorted, y_sorted, J, cluster_sorted, centers, withinss, size);
}
/*#if DEBUG
* std::cout << "backtrack done." << std::endl;
#endif*/
for (int i = 0; i < N; ++i)
{
// Obtain clustering on data in the original order
clusters[order[i]] = cluster_sorted[i];
}
}
else
{
// A single cluster that contains all elements
for (int i = 0; i < N; ++i)
{
clusters[i] = 0;
}
centers = new number[1];
withinss = new number[1];
size = new number[1];
centers[0] = x[0];
withinss[0] = 0;
size[0] = N * (is_equally_weighted ? 1 : y[0]);
}
}